Quasihole Tunneling in Disordered Fractional Quantum Hall Systems

Fractional quantum Hall systems are often described by model wave functions,which are the ground states of pure systems with short-range interaction.A primary example is the Laughlin wave function,which supports Abelian quasiparticles with fractionalized charge.In the presence of disorder,the wave function of the ground state is expected to deviate from the Laughlin form.We study the disorder-driven colla.pse of the quantum Hall state by analyzing the evolution of the ground state and the single-quasihole state.In particular,we demonstrate that the quasihole tunneling amplitude can signal the fractional quantum Hall phase to insulator transition.     

The Laughlin liquid in an external potential

We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N-particle wave functions that have the form of a product of Laughlin states and analytic functions of the N variables. We derive an upper bound to the ground state energy in a confining external potential, matching exactly a recently derived lower bound in the large N limit. Irrespective of the shape of the confining potential, this sharp upper bound can be achieved through a modification of the Laughlin function by suitably arranged quasi-holes.     

Finite clusters of fast-rotating spinless bosons in a harmonic trap

Rapidly rotating two-dimensional ultracold Bose–Einstein condensates of spinless bosons in a harmonic trap have attracted considerable interest during the recent years. It is expected that, in the fast-rotation limit, the system of bosons will exhibit collective behavior similar to that of two-dimensional electrons in the fractional quantum Hall effect regime. It is predicted that the most robust correlated bosonic state in this regime will be the Bose Laughlin state at a half filling factor. An exact treatment of such a state is generally a formidable task due to the inherent many-particle nature of the wave function. We report in this work that a transformation to Jacobi coordinates allows one to obtain much desirable exact analytic closed-form expressions for various quantities of interest corresponding to a Bose Laughlin wave function for various finite systems of particles.     

Signatures of fractional statistics in noise experiments in quantum Hall fluids

The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross-current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a bunching effect, while for higher states in the Jain sequences they should exhibit an "antibunching" effect.     

Microscopic theory of the quantum Hall hierarchy

We solve the quantum Hall problem exactly in a limit and show that the ground states can be organized in a fractal pattern consistent with the Haldane-Halperin hierarchy, and with the global phase diagram. We present wave functions for a large family of states, including those of Laughlin and Jain and also for states recently observed by Pan et al., and show that they coincide with the exact ones in the solvable limit. We submit that they establish an adiabatic continuation of our exact results to the experimentally accessible regime, thus providing a unified approach to the hierarchy states.     

Supersymmetric quantum-Hall effect on a fuzzy supersphere

Supersymmetric quantum-Hall liquids are constructed on a supersphere in a supermonopole background. We derive a supersymmetric generalization of the Laughlin wave function, which is a ground state of a hard-core OSp(1/2) invariant Hamiltonian. We also present excited topological objects, which are fractionally charged deficits made by super Hall currents. Several relations between quantum-Hall systems and their supersymmetric extensions are discussed.     

Correlation-hole induced paired quantum Hall states in the lowest Landau level

A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous interaction that favors chiral p-wave pairing. There are two canonically dual pairing gap functions related by the bosonic Laughlin wave function (Jastrow factor) due to the correlation holes. We find that the ground state is the Moore-Read Pfaffian in the long-wavelength limit for weak Coulomb interactions, a new Pfaffian with an oscillatory pairing function for intermediate interactions, and a Read-Rezayi composite Fermi liquid beyond a critical interaction strength. Our findings are consistent with recent experimental observations of the 1/2 and 1/4 fractional quantum Hall effects in asymmetric wide quantum wells.     

光腔中两组分玻色-爱因斯坦凝聚体的受激辐射特性和量子相变

研究了单模光腔中两组分玻色-爱因斯坦凝聚的基态性质和相关的量子相变.通过利用自旋相干态变换将等效赝自旋哈密顿算符对角化并求得基态能量泛函.基态能量泛函对其经典场变量进行变分并取极小值,得到光子数解和相边界曲线.通过稳定性讨论发现系统除了出现正常相和超辐射相之外,还得到了多稳的宏观量子态;受激辐射来自于原子数反转的集体态,单组分的Dicke系统中并没有此现象;受激辐射只能从一组分的原子中产生,而另外的仍保持在普通超辐射状态.通过调整相关的原子-场耦合强度和频率失谐,超辐射和受激辐射态的顺序可以在原子的两个组分之间互换.     

Rigidity of the Laughlin Liquid

We consider general N-particle wave functions that have the form of a product of the Laughlin state with filling factor \(1/\ell \) and an analytic function of the N variables. This is the most general form of a wave function that can arise through a perturbation of the Laughlin state by external potentials or impurities, while staying in the lowest Landau level and maintaining the strong correlations of the original state. We show that the perturbation can only shift or lower the 1-particle density but nowhere increase it above a maximum value. Consequences of this bound for the response of the Laughlin state to external fields are discussed.     

Quantum Hall ferromagnetic states and spin-orbit interactions in the fractional regime

The competition between the Zeeman energy and the Rashba and Dresselhaus spin-orbit couplings is studied for fractional quantum Hall states by including correlation effects. A transition of the direction of the spin polarization is predicted at specific values of the Zeeman energy. We show that these values can be expressed in terms of the pair-correlation function, and thus provide information about the microscopic ground state. We examine the particular examples of the Laughlin wave functions and the 5/2-Pfaffian state. We also include effects of the nuclear bath.     

Spin-polarized ground state for interacting electrons in two dimensions

We study numerically the ground state magnetization for clusters of interacting electrons in two dimensions in the regime where the single particle wave functions are localized by disorder. It is found that the Coulomb interaction leads to a spontaneous ground state magnetization. For a constant electronic density, the total spin increases linearly with the number of particles, suggesting a ferromagnetic ground state in the thermodynamic limit. The magnetization is suppressed when the single particle states become delocalized.     

Atypical fractional quantum Hall effect in graphene at filling factor 1/3

We study, with the help of exact-diagonalization calculations, a four-component trial wave function that may be relevant for the recently observed graphene fractional quantum Hall state at a filling factor ν(G) = 1/3. Although it is adiabatically connected to a 1/3 Laughlin state in the upper spin branch, with SU(2) valley-isospin ferromagnetic ordering and a completely filled lower spin branch, it reveals physical properties beyond such a state that is the natural ground state for a large Zeeman effect. Most saliently, it possesses at experimentally relevant values of the Zeeman gap low-energy spin-flip excitations that may be unveiled in inelastic light-scattering experiments.     

Quantum Hall fractions in rotating Bose-Einstein condensates

We study the quantum Hall phases that appear in the dilute limit of rotating Bose-Einstein condensates. By exact diagonalization in a spherical geometry we obtain the ground state and low-lying excited states of a small number of bosons as a function of the filling fraction nu, the ratio of the number of bosons to the number of vortices. We show the occurrence of the Jain principal sequence of incompressible liquids for nu=2/3,3/4,4/3,5/4 in addition to the Laughlin state nu=1/2 as well as the Pfaffian state for nu=1. We give gap estimates by finite-size scaling of both charged and neutral excitations.     

Comparison of variational approaches for the exactly solvable 1/r-Hubbard chain

We study Hartree-Fock, Gutzwiller, Baeriswyl, and combined Gutzwiller-Baeriswyl wave functions for the exactly solvable one-dimensional 1/r-Hubbard model. We find that none of these variational wave functions is able to correctly reproduce the physics of the metal-to-insulator transition which occurs in the model for halffilled bands when the interaction strength equals the bandwidth. The many-particle problem to calculate the variational ground state energy for the Baeriswyl and combined Gutzwiller-Baeriswyl wave function is exactly solved for the 1/r-Hubbard model. The latter wave function becomes exact both for small and large interaction strength, but it incorrectly predicts the metal-to-insulator transition to happen at infinitely strong interactions. It is thus seen that neither Hartree-Fock nor an energetically excellent Jastrow-type wave function yield a reliable prediction on the zero temperature phase transition in the one-dimensional 1/r-Hubbard chain.     

A New Differential Formula About Product of Polynomials and Its Application in Multi-electron State Physics

We derive a new differential formula about a kind of product of polynomials and then apply it to analyze some properties of multi-electron state ＂related to Laughlin wave function＂. The entangled state representation for describing electrons in uniform magnetic field is used.     

Strongly Correlated Phases in Rapidly Rotating Bose Gases

We consider a system of trapped spinless bosons interacting with a repulsive potential and subject to rotation. In the limit of rapid rotation and small scattering length, we rigorously show that the ground state energy converges to that of a simplified model Hamiltonian with contact interaction projected onto the Lowest Landau Level. This effective Hamiltonian models the bosonic analogue of the Fractional Quantum Hall Effect (FQHE). For a fixed number of particles, we also prove convergence of states; in particular, in a certain regime we show convergence towards the bosonic Laughlin wavefunction. This is the first rigorous justification of the effective FQHE Hamiltonian for rapidly rotating Bose gases. We review previous results on this effective Hamiltonian and outline open problems.     

Anomalous hydrodynamics of fractional quantum Hall states

We propose a comprehensive framework for quantum hydrodynamics of the fractional quantum Hall (FQH) states. We suggest that the electronic fluid in the FQH regime can be phenomenologically described by the quantized hydrodynamics of vortices in an incompressible rotating liquid. We demonstrate that such hydrodynamics captures all major features of FQH states, including the subtle effect of the Lorentz shear stress. We present a consistent quantization of the hydrodynamics of an incompressible fluid, providing a powerful framework to study the FQH effect and superfluids. We obtain the quantum hydrodynamics of the vortex flow by quantizing the Kirchhoff equations for vortex dynamics.     

Quantum effect in a generalized N-atom Dicke model

We have studied the geometric phase and the sub-Poissonian photon distribution of a generalized N two-level atoms Dicke model in the thermo-dynamical limit and the off-resonant coupling case. It is found that the geometric phase in the ground state is relative to the atom number, the coupling strength between the atom and the light field, the frequency of the electromagnetic wave and the energy difference between two levels of the atom. The photons may exhibit the sub-Poissonian distribution in the ground state.     

Hartree-Fock approximation of bipolaron state in quantum dots and wires

The bipolaronic ground state of two electrons in a spherical quantum dot or a quantum wire with parabolic boundaries is studied in the strong electron-phonon coupling regime. We introduce a variational wave function that can conveniently conform to represent alternative ground state configurations of the two electrons, namely, the bipolaronic bound state, the state of two individual polarons, and two nearby interacting polarons confined by the external potential. In the bipolaron state the electrons are found to be separated by a finite distance about a polaron size. We present the formation and stability criteria of bipolaronic phase in confined media. It is shown that the quantum dot confinement extends the domain of stability of the bipolaronic bound state of two electrons as compared to the bulk geometry, whereas the quantum wire geometry aggravates the formation of stable bipolarons.